One example could be to add a value to the relationship, like a rating or a ranking.
For example a Movie can be seen by many Users and a User can see many Movies. A user can rate the movie they've seen between 0 and 10. So, the join table would have 3 collumns:
- he FK for User
- the FK for Movie
- the numerical value of the rating by that particular User for that particualr Movie.